English people keep going on about how immigrants should assimilate. It's quite a big issue here. Though I don't hear it from the Scots nor the Welsh and that may be because they don't want to integrate either.
The English have mostly shrugged off the overt racism of the recent past, but they are still quite racist - but not just racist, they tend to fear anyone who is different. They don't like foreigners, generally speaking, even European foreigners who they superficially resemble, but they may like you on a one-to-one basis. Once they get to know you and relax you'll know because they start making ironic comments and jokes about race (the English have special jokes for Scots, Welsh, Germans, Belgians, French, Dutch, Spanish, Scandinavians and East Europeans; as well as race - i.e. colour - jokes though these have gone a bit deeper underground). Often the racism is quite casual and unremarkable. 'White' and 'black' are still acceptable, even politically correct, terms here. After 8 years I'm starting to get used to it, but I refuse to identify myself as 'white'. When they say assimilate, it means "don't be a foreigner, because we don't like foreigners." I recognise this to some extent because it's a feature of living on an island - and of course there is a long history of conflict with the mainland.
What the English fear, as always, is an invasion. They haven't forgotten for forgiven the Norman Conquest (though most have forgotten that William of Orange also invaded in 1688). They certainly haven't forgotten the Battle of Britain - and it has become one of the defining moments in modern British history. Not only is johnny foreigner a bit of a rum chap, but he bally well wants to take this green and pleasant land. The English fear foreigners en mass a lot more than individually - partly from having been at war with one nation or another for the last 1000 years. At the moment England has high immigration and it is a bone of contention. Having joined the European Economic Community and more recently the European Union Britain has tended to cut it self off from it's former colonies, the Commonwealth Games not-withstanding, and open it's doors to Europe (which is full of foreigners). It may well be that the present government is more able to deal with mass immigration than the last. Hopefully this will mean much less support for far-right groups!
English culture is complex. Life is lived according to a multitude of unwritten rules. To fully assimilate is very difficult. And I'm not saying they are bad people. They aren't. They're just being themselves, and I think it's similar everywhere. I try to take part in the life of the nation (to the extent I can) and I vote in elections both local and national. If I could afford to buy citizenship (£950 last time I looked) I would buy it, but I can't afford it. I'd be happy to call myself a citizen. But if I became a citizen what would I be? The usual overarching adjective for English, Welsh, Scots and Northern Irish is British. So I might become British to some extent, but I don't think anyone can become English except by being born and growing up here. One can only become a pale imitation, a mockery. And they'll only hate you for that. I might add that anyone who has met an English person abroad will know that they are often the last people to assimilate, because perhaps they still think you should assimilate to them even when they are a minority of one!
It's just not that easy to blend in as a foreigner here - any conversation with a new acquaintance lasting more than 5 minutes usually involves being asked if I'm an Australian! It says something that most English people are unable to distinguish between these two accents, or in some cases between either of those two and South African. They all know about the countries, and most express affection for one or the other, and a desire to go there, and they all know Kiwis and Aussies because we're everywhere. But they can't make a distinction between us - just as foreigners look the same; colonials sound the same. I'm constantly teased about my accent by my friends, who to be fair also tease the Mancunians I live with about their accents. I can't do much about my accent without becoming affected and inauthentic, which would probably be seen as an ever greater barrier to assimilation.
So yes we might try to assimilate, but there are always going to be limits - limits imposed by the English themselves which grow out of English culture. I only write this in response to the constant harping on assimilation - which as a foreigner begins to irritate. Although I'm kind of stuck, I do like living here for the most part, and given the circumstances have a good life. I have a great deal of affection for the English, and I suppose they are not alone in having blind spots.
My one suggestion for helping assimilation is make citizenship cheaper - it could be quite hard to get citizenship, and have all kinds of requirements, but don't make it so expensive. I don't imagine it costs £950 to process a form and do a CRB check. If it were a bank charge we could complain about it not representing the true cost of the transaction! Make it realistic. Having passed the Life in the UK test, and been a good probationary citizen for some years, make it easy to identify with the place as home, but easing the journey to citizenship.